Finite Group Databasebeta

← C113×#18705 #43286725

Subgroups — C113×#18705 #43286725

Order 28928.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3546C211yesmaximal, characteristic
2C113×#3252C211yesmaximal, characteristic, complemented
3C113×#3235C211yesmaximal, characteristic, complemented
4C113×#3167C211yesmaximal, characteristic, complemented
5C113×#1654C211yesmaximal, characteristic, complemented
6C113×#1652C211yesmaximal, characteristic, complemented
7C113×#1641C211yesmaximal, characteristic, complemented
8C113×#1639C211yesmaximal, characteristic, complemented
9C113×#1638C211yesmaximal, characteristic, complemented
10C113×#1635C211yesmaximal, characteristic, complemented
11C113×#1631C211yesmaximal, characteristic, complemented
12C113×#1629C211yesmaximal, characteristic, complemented
13C113×#1557C211yesmaximal, characteristic, complemented
14C113×#1494C211yesmaximal, characteristic, complemented
15C113×#1492C211yesmaximal, characteristic, complemented
16#560×C113—22no—
17#556×C113C2211yescharacteristic
18#553×C113—21no—
19#550×C113—21no—
20#550×C113C2211yescharacteristic
21#547×C113C2211yescharacteristic
22#546×C113—21no—
23#546×C113—21no—
24D42×C113C2211yescharacteristic
25#542×C113—21no—
26#538×C113—22no—
27#537×C113—21no—
28#535×C113—21no—
29#535×C113—21no—
30#533×C113C2211yescharacteristic, complemented
31#532×C113C2211yescharacteristic
32#532×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34#501×C113—21no—
35#498×C113C2211yescharacteristic, complemented
36#492×C113C2211yescharacteristic
37#490×C113—21no—
38#487×C113C2211yescharacteristic, complemented
39#486×C113C2211yescharacteristic
40#482×C113—21no—
41#482×C113—21no—
42#479×C113—21no—
43#477×C113C2211yescharacteristic, complemented
44#476×C113C2211yescharacteristic
45#476×C113C2211yescharacteristic
46#476×C113C2211yescharacteristic, complemented
47#474×C113C2211yescharacteristic
48#474×C113C2211yescharacteristic, complemented
49#470×C113—21no—
50#468×C113—21no—
51#465×C113—22no—
52#464×C113—21no—
53#462×C113C2211yescharacteristic, complemented
54#461×C113C2211yescharacteristic
55C4×SD16×C113—22no—
56#432×C113C2211yescharacteristic, complemented
57#423×C113C2211yescharacteristic, complemented
58C2×C4×C8×C113C2211yescharacteristic, complemented
59#332×C113C2211yescharacteristic, complemented
60#332×C113C2211yescharacteristic, complemented
61#331×C113C2211yescharacteristic
62#331×C113C2211yescharacteristic
63Q8⋊C8×C113C2211yescharacteristic, complemented
64Q8⋊C8×C113C2211yescharacteristic, complemented
65D4⋊C8×C113C2211yescharacteristic
66D4⋊C8×C113C2211yescharacteristic
67D4⋊C8×C113C2211yescharacteristic
68D4⋊C8×C113C2211yescharacteristic
69D4⋊C8×C113C2211yescharacteristic, complemented
70D4⋊C8×C113C2211yescharacteristic, complemented
71C2×#41×C113—21no—
72C2×#41×C113—21no—
73C2×#41×C113—21no—
74C2×#41×C113—21no—
75C22×D4×C113—21no—
76C22×D4×C113—21no—
77C2×Q16×C113—21no—
78C2×SD16×C113—22no—
79C2×SD16×C113—21no—
80C2×M16×C113—21no—
81C22×C8×C113—21no—
82C4⋊Q8×C113D411yescharacteristic
83C4⋊Q8×C113C2311yescharacteristic
84C4⋊Q8×C113C2311yescharacteristic
85C4⋊Q8×C113C2311yescharacteristic
86#127×C113—22no—
87#127×C113—21no—
88#127×C113D411yescharacteristic
89#127×C113C2311yescharacteristic
90#126×C113—22no—
91#126×C113—22no—
92#126×C113—21no—
93#125×C113—21no—
94#125×C113D411yescharacteristic
95#124×C113—22no—
96#124×C113—21no—
97#124×C113—21no—
98#124×C113—21no—
99#124×C113D411yescharacteristic
100#123×C113—22no—
101#123×C113—22no—
102#123×C113—21no—
103#123×C113—22no—
104C22⋊Q8×C113—22no—
105C22⋊Q8×C113—21no—
106C22⋊Q8×C113—21no—
107C22⋊Q8×C113—21no—
108C22⋊Q8×C113—21no—
109C22⋊Q8×C113D411yescharacteristic
110#121×C113—22no—
111#121×C113—22no—
112#121×C113—22no—
113#121×C113—22no—
114#121×C113—22no—
115#121×C113—21no—
116#121×C113—22no—
117#121×C113—21no—
118#121×C113—21no—
119#121×C113—21no—
120#121×C113—21no—
121#121×C113—21no—
122#121×C113D411yescharacteristic
123#121×C113D411yescharacteristic
124#121×C113D411yescharacteristic
125#121×C113D412yes—
126#120×C113—22no—
127#120×C113—22no—
128#120×C113—22no—
129#120×C113—22no—
130C4×Q8×C113—21no—
131C4×Q8×C113—21no—
132C4×Q8×C113—21no—
133C4×Q8×C113C2311yescharacteristic
134C4×D4×C113—22no—
135C4×D4×C113—21no—
136C4×D4×C113—21no—
137C4×D4×C113—21no—
138C4×D4×C113—21no—
139C4×D4×C113D412yes—
140C4×D4×C113C2311yescharacteristic
141C4×D4×C113C2311yescharacteristic
142C4×D4×C113C2311yescharacteristic
143#117×C113—21no—
144#117×C113—21no—
145#117×C113—21no—
146C2×C4⋊C4×C113—21no—
147C2×C22⋊C4×C113—22no—
148C2×C42×C113C2311yescharacteristic
149#107×C113—21no—
150#107×C113—21no—
151#107×C113—21no—
152#106×C113—22no—
153#106×C113—21no—
154#106×C113—21no—
155#106×C113—21no—
156C4⋊C8×C113—21no—
157C4⋊C8×C113C2311yescharacteristic
158C4⋊C8×C113C2311yescharacteristic
159C4⋊C8×C113C2311yescharacteristic
160C4⋊C8×C113C2311yescharacteristic
161#103×C113—21no—
162#103×C113—22no—
163#103×C113—21no—
164#103×C113—21no—
165#102×C113—22no—
166#102×C113—21no—
167#102×C113—21no—
168#102×C113—21no—
169#102×C113—21no—
170#102×C113—21no—
171C22⋊C8×C113—21no—
172#97×C113—21no—
173C4×C8×C113—21no—
174C4×C8×C113C2311yescharacteristic
175C4×C8×C113C2311yescharacteristic
176C24×C113—22no—
177#41×C113—81no—
178#41×C113—81no—
179#41×C113—81no—
180#41×C113—81no—
181#41×C113—81no—
182#41×C113—81no—
183#41×C113—81no—
184#41×C113—81no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113—21no—
188C2×Q8×C113—21no—
189C2×Q8×C113C2×D411yescharacteristic
190C2×D4×C113—22no—
191C2×D4×C113—22no—
192C2×D4×C113—22no—
193C2×D4×C113—22no—
194C2×D4×C113—22no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—22no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—81no—
204C2×D4×C113—81no—
205C2×D4×C113—81no—
206C2×D4×C113—81no—
207C2×D4×C113C2×D411yescharacteristic
208C2×D4×C113C2×D411yescharacteristic
209C2×D4×C113C2×D411yescharacteristic
210C2×D4×C113C2×D412yes—
211C22×C4×C113—22no—
212C22×C4×C113—22no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—22no—
217C22×C4×C113C2×D411yescharacteristic
218C22×C4×C113C2×D411yescharacteristic
219C22×C4×C113C2×D411yescharacteristic
220Q16×C113—81no—
221SD16×C113—44no—
222SD16×C113—81no—
223M16×C113—81no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—42no—
231C4⋊C4×C113—22no—
232C4⋊C4×C113—22no—
233C4⋊C4×C113—21no—
234C4⋊C4×C113—21no—
235C4⋊C4×C113—21no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—41no—
244C4⋊C4×C113—41no—
245C4⋊C4×C113C2×D411yescharacteristic
246C4⋊C4×C113C2×D412yes—
247C4⋊C4×C113C2×D411yescharacteristic
248C4⋊C4×C113C2×D411yescharacteristic
249C4⋊C4×C113C2×D411yescharacteristic
250C22⋊C4×C113—22no—
251C22⋊C4×C113—22no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—22no—
254C22⋊C4×C113—22no—
255C22⋊C4×C113—21no—
256C22⋊C4×C113—21no—
257C22⋊C4×C113—21no—
258C22⋊C4×C113—21no—
259C22⋊C4×C113—21no—
260C22⋊C4×C113—21no—
261C22⋊C4×C113—22no—
262C22⋊C4×C113—22no—
263C22⋊C4×C113—21no—
264C22⋊C4×C113—21no—
265C22⋊C4×C113—21no—
266C22⋊C4×C113—41no—
267C42×C113—22no—
268C42×C113—21no—
269C42×C113—41no—
270C42×C113C2×D411yescharacteristic
271C42×C113C2×D411yescharacteristic
272C42×C113C2×D411yescharacteristic
273C42×C113C2411yescharacteristic
274C23×C113—21no—
275C23×C113—21no—
276C23×C113—22no—
277C23×C113—21no—
278C23×C113—82no—
279C23×C113—82no—
280C23×C113—82no—
281C23×C113#12011yescharacteristic
282Q8×C113—21no—
283Q8×C113—21no—
284Q8×C113—42no—
285Q8×C113—41no—
286Q8×C113—41no—
287Q8×C113—41no—
288Q8×C113—41no—
289Q8×C113—81no—
290D4×C113—21no—
291D4×C113—21no—
292D4×C113—21no—
293D4×C113—21no—
294D4×C113—21no—
295D4×C113—21no—
296D4×C113—42no—
297D4×C113—41no—
298D4×C113—41no—
299D4×C113—41no—
300D4×C113—41no—
301D4×C113—81no—
302D4×C113—81no—
303D4×C113—81no—
304D4×C113—82no—
305D4×C113—81no—
306D4×C113—81no—
307D4×C113—82no—
308D4×C113—82no—
309D4×C113—82no—
310D4×C113—82no—
311D4×C113—82no—
312C2×C4×C113—21no—
313C2×C4×C113—21no—
314C2×C4×C113—21no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—22no—
320C2×C4×C113—21no—
321C2×C4×C113—21no—
322C2×C4×C113—41no—
323C2×C4×C113—41no—
324C2×C4×C113—41no—
325C2×C4×C113—41no—
326C2×C4×C113—41no—
327C2×C4×C113—41no—
328C2×C4×C113—41no—
329C2×C4×C113—41no—
330C2×C4×C113—41no—
331C2×C4×C113—82no—
332C2×C4×C113—82no—
333C2×C4×C113—82no—
334C2×C4×C113#12011yescharacteristic
335C2×C4×C113#12011yescharacteristic
336C2×C4×C113#12011yescharacteristic
337C2×C4×C113C22×D411yescharacteristic
338C2×C4×C113C22×D411yescharacteristic
339C2×C4×C113C22×D411yescharacteristic
340C8×C113—22no—
341C8×C113—41no—
342C8×C113—41no—
343C8×C113—41no—
344C8×C113—41no—
345C8×C113—41no—
346C22×C113—21no—
347C22×C113—21no—
348C22×C113—21no—
349C22×C113—41no—
350C22×C113—41no—
351C22×C113—42no—
352C22×C113—41no—
353C22×C113—41no—
354C22×C113—41no—
355C22×C113—42no—
356C22×C113—41no—
357C22×C113—42no—
358C22×C113—41no—
359C22×C113—41no—
360C22×C113—41no—
361C22×C113—164no—
362C22×C113C2×#12011yescharacteristic
363C4×C113—21no—
364C4×C113—21no—
365C4×C113—21no—
366C4×C113—21no—
367C4×C113—41no—
368C4×C113—42no—
369C4×C113—41no—
370C4×C113—41no—
371C4×C113—41no—
372C4×C113—41no—
373C4×C113—81no—
374C4×C113—81no—
375C4×C113#57611yescharacteristic
376C4×C113#57711yescharacteristic
377C4×C113#57711yescharacteristic
378C4×C113#57711yescharacteristic
379#18705C11311yesmaximal, characteristic, direct product factor, Sylow
380C2×C113—41no—
381C2×C113—81no—
382C2×C113—82no—
383C2×C113—81no—
384C2×C113—81no—
385C2×C113#300911yescharacteristic
386C2×C113#301211yescharacteristic
387C2×C113#301811yescharacteristic
388#3546C2×C11311yescharacteristic
389#3252C2×C11311yescharacteristic, complemented
390#3235C2×C11311yescharacteristic, complemented
391#3167C2×C11311yescharacteristic, complemented
392#1654C2×C11311yescharacteristic, complemented
393#1652C2×C11311yescharacteristic, complemented
394#1641C2×C11311yescharacteristic, complemented
395#1639C2×C11311yescharacteristic, complemented
396#1638C2×C11311yescharacteristic, complemented
397#1635C2×C11311yescharacteristic, complemented
398#1631C2×C11311yescharacteristic, complemented
399#1629C2×C11311yescharacteristic, complemented
400#1557C2×C11311yescharacteristic, complemented
401#1494C2×C11311yescharacteristic, complemented
402#1492C2×C11311yescharacteristic, complemented
403C113#1870511yescharacteristic, direct product factor, Sylow
404#560—22no—
405#556C22×C11311yescharacteristic
406#553—21no—
407#550—21no—
408#550C22×C11311yescharacteristic
409#547C22×C11311yescharacteristic
410#546—21no—
411#546—21no—
412D42C22×C11311yescharacteristic
413#542—21no—
414#538—22no—
415#537—21no—
416#535—21no—
417#535—21no—
418#533C22×C11311yescharacteristic, complemented
419#532C22×C11311yescharacteristic
420#532C22×C11311yescharacteristic
421#529C22×C11311yescharacteristic
422#501—21no—
423#498C22×C11311yescharacteristic, complemented
424#492C22×C11311yescharacteristic
425#490—21no—
426#487C22×C11311yescharacteristic, complemented
427#486C22×C11311yescharacteristic
428#482—21no—
429#482—21no—
430#479—21no—
431#477C22×C11311yescharacteristic, complemented
432#476C22×C11311yescharacteristic
433#476C22×C11311yescharacteristic
434#476C22×C11311yescharacteristic, complemented
435#474C22×C11311yescharacteristic
436#474C22×C11311yescharacteristic, complemented
437#470—21no—
438#468—21no—
439#465—22no—
440#464—21no—
441#462C22×C11311yescharacteristic, complemented
442#461C22×C11311yescharacteristic
443C4×SD16—22no—
444#432C22×C11311yescharacteristic, complemented
445#423C22×C11311yescharacteristic, complemented
446C2×C4×C8C22×C11311yescharacteristic, complemented
447#332C22×C11311yescharacteristic, complemented
448#332C22×C11311yescharacteristic, complemented
449#331C22×C11311yescharacteristic
450#331C22×C11311yescharacteristic
451Q8⋊C8C22×C11311yescharacteristic, complemented
452Q8⋊C8C22×C11311yescharacteristic, complemented
453D4⋊C8C22×C11311yescharacteristic
454D4⋊C8C22×C11311yescharacteristic
455D4⋊C8C22×C11311yescharacteristic
456D4⋊C8C22×C11311yescharacteristic
457D4⋊C8C22×C11311yescharacteristic, complemented
458D4⋊C8C22×C11311yescharacteristic, complemented
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C22×D4—21no—
464C22×D4—21no—
465C2×Q16—21no—
466C2×SD16—22no—
467C2×SD16—21no—
468C2×M16—21no—
469C22×C8—21no—
470C4⋊Q8D4×C11311yescharacteristic
471C4⋊Q8C23×C11311yescharacteristic
472C4⋊Q8C23×C11311yescharacteristic
473C4⋊Q8C23×C11311yescharacteristic
474#127—22no—
475#127—21no—
476#127D4×C11311yescharacteristic
477#127C23×C11311yescharacteristic
478#126—22no—
479#126—22no—
480#126—21no—
481#125—21no—
482#125D4×C11311yescharacteristic
483#124—22no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124D4×C11311yescharacteristic
488#123—22no—
489#123—22no—
490#123—21no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C11311yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—21no—
504#121—22no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121D4×C11311yescharacteristic
511#121D4×C11311yescharacteristic
512#121D4×C11311yescharacteristic
513#121D4×C11312yes—
514#120—22no—
515#120—22no—
516#120—22no—
517#120—22no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8C23×C11311yescharacteristic
522C4×D4—22no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4D4×C11312yes—
528C4×D4C23×C11311yescharacteristic
529C4×D4C23×C11311yescharacteristic
530C4×D4C23×C11311yescharacteristic
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C22⋊C4—22no—
536C2×C42C23×C11311yescharacteristic
537#107—21no—
538#107—21no—
539#107—21no—
540#106—22no—
541#106—21no—
542#106—21no—
543#106—21no—
544C4⋊C8—21no—
545C4⋊C8C23×C11311yescharacteristic
546C4⋊C8C23×C11311yescharacteristic
547C4⋊C8C23×C11311yescharacteristic
548C4⋊C8C23×C11311yescharacteristic
549#103—21no—
550#103—22no—
551#103—21no—
552#103—21no—
553#102—22no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559C22⋊C8—21no—
560#97—21no—
561C4×C8—21no—
562C4×C8C23×C11311yescharacteristic
563C4×C8C23×C11311yescharacteristic
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C11311yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C11311yescharacteristic
596C2×D4C2×D4×C11311yescharacteristic
597C2×D4C2×D4×C11311yescharacteristic
598C2×D4C2×D4×C11312yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C11311yescharacteristic
606C22×C4C2×D4×C11311yescharacteristic
607C22×C4C2×D4×C11311yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C11311yescharacteristic
634C4⋊C4C2×D4×C11312yes—
635C4⋊C4C2×D4×C11311yescharacteristic
636C4⋊C4C2×D4×C11311yescharacteristic
637C4⋊C4C2×D4×C11311yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C11311yescharacteristic
659C42C2×D4×C11311yescharacteristic
660C42C2×D4×C11311yescharacteristic
661C42C24×C11311yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23#120×C11311yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—82no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4#120×C11311yescharacteristic
723C2×C4#120×C11311yescharacteristic
724C2×C4#120×C11311yescharacteristic
725C2×C4C22×D4×C11311yescharacteristic
726C2×C4C22×D4×C11311yescharacteristic
727C2×C4C22×D4×C11311yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×#120×C11311yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4#576×C11311yescharacteristic
764C4#577×C11311yescharacteristic
765C4#577×C11311yescharacteristic
766C4#577×C11311yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C113×#300911yescharacteristic
773C2C113×#301211yescharacteristic
774C2C113×#301811yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C113×#3252C2semidirect
3. C113×#3235C2semidirect
4. C113×#3167C2semidirect
5. C113×#1654C2semidirect
6. C113×#1652C2semidirect
7. C113×#1641C2semidirect
8. C113×#1639C2semidirect
9. C113×#1638C2semidirect
10. C113×#1635C2semidirect
11. C113×#1631C2semidirect
12. C113×#1629C2semidirect
13. C113×#1557C2semidirect
14. C113×#1494C2semidirect
15. C113×#1492C2semidirect
30. #533×C113C22semidirect
35. #498×C113C22semidirect
38. #487×C113C22semidirect
43. #477×C113C22semidirect
46. #476×C113C22semidirect
48. #474×C113C22semidirect
53. #462×C113C22semidirect
56. #432×C113C22semidirect
57. #423×C113C22semidirect
58. C2×C4×C8×C113C22semidirect
59. #332×C113C22semidirect
60. #332×C113C22semidirect
63. Q8⋊C8×C113C22semidirect
64. Q8⋊C8×C113C22semidirect
69. D4⋊C8×C113C22semidirect
70. D4⋊C8×C113C22semidirect
379. #18705C113direct (N × H)
389. #3252C2×C113semidirect
390. #3235C2×C113semidirect
391. #3167C2×C113semidirect
392. #1654C2×C113semidirect
393. #1652C2×C113semidirect
394. #1641C2×C113semidirect
395. #1639C2×C113semidirect
396. #1638C2×C113semidirect
397. #1635C2×C113semidirect
398. #1631C2×C113semidirect
399. #1629C2×C113semidirect
400. #1557C2×C113semidirect
401. #1494C2×C113semidirect
402. #1492C2×C113semidirect
403. C113#18705direct (N × H)
418. #533C22×C113semidirect
423. #498C22×C113semidirect
426. #487C22×C113semidirect
431. #477C22×C113semidirect
434. #476C22×C113semidirect
436. #474C22×C113semidirect
441. #462C22×C113semidirect
444. #432C22×C113semidirect
445. #423C22×C113semidirect
446. C2×C4×C8C22×C113semidirect
447. #332C22×C113semidirect
448. #332C22×C113semidirect
451. Q8⋊C8C22×C113semidirect
452. Q8⋊C8C22×C113semidirect
457. D4⋊C8C22×C113semidirect
458. D4⋊C8C22×C113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C113×#35462
C113×#32522
C113×#32352
C113×#31672
C113×#16542
C113×#16522
C113×#16412
C113×#16392
C113×#16382
C113×#16352
C113×#16312
C113×#16292
C113×#15572
C113×#14942
C113×#14922
#18705113